Simple Interest
Math MCQs

Question :    What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?

Correct Answer  $4290

Solution & Explanation

Solution

Given,

Principal (P) = $3900

Rate of Simple Interest (SI) = 5%

Time (t) = 2 years

Thus, Amount (A) = ?

The Rate of Interest is always calculated per annum, i.e. per year.

Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% per annum.

Method (1) Using Formula

Calculation of Simple Interest

Formula to Calculate Simple Interest

Simple Interest (SI) = Principal × Rate × Time

Thus, Simple Interest (SI) = $3900 × 5% × 2

= $3900 ×⁵/₁₀₀ × 2

= ^{3900 × 5 × 2}/₁₀₀

= ^{19500 × 2}/₁₀₀

= ³⁹⁰⁰⁰/₁₀₀

= $390

Thus, Simple Interest = $390

Calculation of Amount

The total money paid to the lender by a borrower is called the Amount.

In other words, sum of priciple and interest is called the Amount.

Formula to Calculate the Amount

Amount = Principal + Interest

Thus, Amount = $3900 + $390

= $4290

Thus, Amount to be paid = $4290 Answer

Method (2)

Calculation of Amount when Principal, Rate of Simple Interest and Time are given

Calculation of Amount directly using Principal, SI, and Time

Formula to calculate the Amount

Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)

⇒ A = P + PRT

Here in the question, P = $3900

Rate of Simple Interest (SI) or (R) = 5%

And, Time (t) = 2 years

Thus, Amount (A)

= $3900 + ($3900 × 5% × 2)

= $3900 + ($3900 ×⁵/₁₀₀ × 2)

= $3900 + (^{3900 × 5 × 2}/₁₀₀)

= $3900 + (^{19500 × 2}/₁₀₀)

= $3900 + (³⁹⁰⁰⁰/₁₀₀)

= $3900 + $390 = $4290

Thus, Amount (A) to be paid = $4290 Answer

Method (3) Unitary Method

Calculation of Amount using Unitary Method

Calculation of Interest using Unitary Method

Here, given Rate of Simple Interest = 5%

This, means, $5 per $100 per year

∵ For $100, the simple interest for 1 year = $5

∴ For $1, the simple interest for 1 year = ⁵/₁₀₀

∴ For $3900, the simple interest in 1 year

= ⁵/₁₀₀ × 3900

= ^{5 × 3900}/₁₀₀

= ¹⁹⁵⁰⁰/₁₀₀ = $195

Thus, simple interest for 1 year = $195

Therefore, simple interest for 2 years

= Simple interest for 1 year × 2

= $195 × 2 = $390

Thus, Simple Interest (SI) = $390

Calculation of Amount

Amount = Principal + Interest

Thus, Amount = $3900 + $390

= $4290

Thus, Amount to be paid = $4290 Answer

Similar Questions

(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(2) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(3) Betty had to pay $4887.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?

(6) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?

(7) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.

(10) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.